A generalization of Dirichlet's unit theorem

• Autorzy: Paul Fili , Zachary Miner
• Języki publikacji: EN

Abstrakty

EN

We generalize Dirichlet's S-unit theorem from the usual group of S-units of a number field K to the infinite rank group of all algebraic numbers having nontrivial valuations only on places lying over S. Specifically, we demonstrate that the group of algebraic S-units modulo torsion is a ℚ-vector space which, when normed by the Weil height, spans a hyperplane determined by the product formula, and that the elements of this vector space which are linearly independent over ℚ retain their linear independence over ℝ.

Kategorie tematyczne

• 11R04: Algebraic numbers; rings of algebraic integers
• 46E30: Spaces of measurable functions ( L p -spaces, Orlicz spaces, K\"othe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
• 11R27: Units and factorization

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2014
• Tom: 162
• Numer: 4
• Strony: 355-368

Daty

wydano

2014

Twórcy

autor

Paul Fili

• Department of Mathematics, University of Rochester, Rochester, NY 14627, U.S.A.

autor

Zachary Miner

• Department of Mathematics, University of Texas at Austin, Austin, TX 78712, U.S.A.

Identyfikatory

DOI

10.4064/aa162-4-3